Sard properties for polynomial maps in infinite dimension and applications to the sub-Riemannian Sard conjecture

par Daniele Tiberio (SISSA)

mardi 5 nov. 2024, 11:00 → 12:00 Europe/Paris

salle de conférences

I will consider "polynomial maps" from an infinite-dimensional Hilbert space to a finite-dimensional Euclidean space (for instance, the endpoint maps of some control systems). It is well-known that the classical Sard theorem is false in this setting, and a general theory is still lacking. I will present sharp Sard-type theorems for these maps, obtained by combining a functional analysis approach with new tools in semialgebraic geometry. As an application, I will present new results on the sub-Riemannian Sard conjecture in Carnot groups (the simplest sub-Riemannian geometries). This talk is based on a work in collaboration with Antonio Lerario and Luca Rizzi.